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In mathematics, the '''random Fibonacci sequence''' is a stochastic analogue of the [[Fibonacci sequence]] defined by the [[recurrence relation]] ''f''<sub>''n''</sub> = ''f''<sub>''n''−1</sub> ± ''f''<sub>''n''−2</sub>, where the signs + or − are chosen [[Bernoulli distribution|at random]] with equal probability 1/2, [[Independence (probability theory)|independently]] for different ''n''. By a theorem of [[Harry Kesten]] and [[Hillel Furstenberg]], random recurrent sequences of this kind grow at a certain [[exponential growth|exponential rate]], but it is difficult to compute the rate explicitly. In 1999, [[Divakar Viswanath]] showed that the growth rate of the random Fibonacci sequence is equal to 1.1319882487943…{{OEIS|A0416}}, a [[mathematical constant]] that was later named '''Viswanath's constant'''.<ref>{{Cite journal | last1 = Viswanath | first1 = D. | title = Random Fibonacci sequences and the number $1.13198824\dots$ | doi = 10.1090/S0025-5718-99-01145-X | journal = Mathematics of Computation | volume = 69 | issue = 231 | pages = 1131–1155 | year = 1999 | pmid = | pmc = }}</ref><ref>{{Cite journal | last1 = Oliveira | first1 = J. O. B. | last2 = De Figueiredo | first2 = L. H. | journal = Reliable Computing | volume = 8 | issue = 2 | pages = 131 |title=Interval Computation of Viswanath's Constant| year = 2002 | doi = 10.1023/A:1014702122205 | pmid = | pmc = }}</ref><ref>{{Cite journal | last1 = Makover | first1 = E. | last2 = McGowan | first2 = J. | doi = 10.1016/j.jnt.2006.01.002 | title = An elementary proof that random Fibonacci sequences grow exponentially | journal = Journal of Number Theory | volume = 121 | pages = 40 | year = 2006 | pmid = | pmc = |arxiv=math.NT/0510159}}</ref>
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